Question 1069630
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{{{(10*9)/2}}} = 45.


Each of 10 friends handshakes with each and all other 9 friends,


and for each two pairs (a,b) and (b,a) we register only ONE handshake.


Therefore, we multiply 10 by 9 and then divide by 2.



The outcome is the same as the number of combinations of 10 items taken 2 at a time.